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Simplifying 0 = -7x2 + 84x + -50 Reorder the terms: 0 = -50 + 84x + -7x2 Solving 0 = -50 + 84x + -7x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + -84x + 7x2 = -50 + 84x + -7x2 + 50 + -84x + 7x2 Reorder the terms: 50 + -84x + 7x2 = -50 + 50 + 84x + -84x + -7x2 + 7x2 Combine like terms: -50 + 50 = 0 50 + -84x + 7x2 = 0 + 84x + -84x + -7x2 + 7x2 50 + -84x + 7x2 = 84x + -84x + -7x2 + 7x2 Combine like terms: 84x + -84x = 0 50 + -84x + 7x2 = 0 + -7x2 + 7x2 50 + -84x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 50 + -84x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 7.142857143 + -12x + x2 = 0 Move the constant term to the right: Add '-7.142857143' to each side of the equation. 7.142857143 + -12x + -7.142857143 + x2 = 0 + -7.142857143 Reorder the terms: 7.142857143 + -7.142857143 + -12x + x2 = 0 + -7.142857143 Combine like terms: 7.142857143 + -7.142857143 = 0.000000000 0.000000000 + -12x + x2 = 0 + -7.142857143 -12x + x2 = 0 + -7.142857143 Combine like terms: 0 + -7.142857143 = -7.142857143 -12x + x2 = -7.142857143 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -7.142857143 + 36 Reorder the terms: 36 + -12x + x2 = -7.142857143 + 36 Combine like terms: -7.142857143 + 36 = 28.857142857 36 + -12x + x2 = 28.857142857 Factor a perfect square on the left side: (x + -6)(x + -6) = 28.857142857 Calculate the square root of the right side: 5.371884479 Break this problem into two subproblems by setting (x + -6) equal to 5.371884479 and -5.371884479.Subproblem 1
x + -6 = 5.371884479 Simplifying x + -6 = 5.371884479 Reorder the terms: -6 + x = 5.371884479 Solving -6 + x = 5.371884479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.371884479 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.371884479 + 6 x = 5.371884479 + 6 Combine like terms: 5.371884479 + 6 = 11.371884479 x = 11.371884479 Simplifying x = 11.371884479Subproblem 2
x + -6 = -5.371884479 Simplifying x + -6 = -5.371884479 Reorder the terms: -6 + x = -5.371884479 Solving -6 + x = -5.371884479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.371884479 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.371884479 + 6 x = -5.371884479 + 6 Combine like terms: -5.371884479 + 6 = 0.628115521 x = 0.628115521 Simplifying x = 0.628115521Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.371884479, 0.628115521}
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